Baum's forward-backward algorithm revisited

Devijver, Pierre A.

doi:10.1016/0167-8655(85)90023-6

Cited by 146 publications

(83 citation statements)

References 4 publications

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“…In this case, the probability distribution of r is given by: P(r) = P(r(1)) t=T t=2 P(r(t) | r(t − 1)) where P(r(t) | r(t − 1)) is given by a transition matrix independent of t. The main advantage of considering a Markov model is that P(r | X; θ) can be calculated by an efficient forward-backward algorithm [7], making ICE method applicable [10].…”

Section: Hidden Process R Modelmentioning

confidence: 99%

An extension of the ICA model using latent variables

Rafi

Castella

Pieczynski

2011

2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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The Independent Component Analysis (ICA) model is extended to the case where the components are not necessarily independent: depending on the value a hidden latent process at the same time, the unknown components of the linear mixture are assumed either mutually independent or dependent. We propose for this model a separation method which combines: (i) a classical ICA separation performed using the set of samples whose components are conditionally independent, and (ii) a method for estimation of the latent process. The latter task is performed by Iterative Conditional Estimation (ICE). It is an estimation technique in the case of incomplete data, which is particularly appealing because it requires only weak conditions. Finally, simulations validate our method and show that the separation quality is improved for sources generated according to our model.

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Section: Hidden Process R Modelmentioning

confidence: 99%

An extension of the ICA model using latent variables

Rafi

Castella

Pieczynski

2011

2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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“…At the 1984 ICPR, Pierre extended this to take into account the information from any number of succeeding patterns by adding an iterative backward pass [6,]. He subsequently improved the numerical stability of Baum's HMM training algorithm by computing joint rather than conditional probabilities [7]. Already then his interest lay in Markov meshes and MRFs for image processing, so he avoided any assumptions that applied only to 1-D.…”

Section: Markov Algorithmsmentioning

confidence: 99%

Estimation, Learning, and Adaptation: Systems That Improve with Use

Nagy¹

2012

Lecture Notes in Computer Science

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Abstract. The accuracy of automated classification (labeling) of single patterns, especially printed, hand-printed, or handwritten characters, has leveled off. Further gains in accuracy require classifying sequences of patterns. Linguistic context, already widely used, relies on 1-D lexical and syntactic constraints. Style-constrained classification exploits the shape-similarity of sets of same-source (isogenous) characters of either the same or different classes. For understanding tables and forms, 2-D structural and relational constraints are necessary. Applications of pattern recognition that do not exceed the limits of human senses and cognition can benefit from green interaction wherein operator corrections are recycled to the classifier.

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“…There exist at least 3 ways to compute the likelihood defined by (49): the forward-backward algorithm defined by [15] (and improved by [48]), the filter defined by [72], and the matrix form that we now present.…”

Section: Computation Of the Likelihoodmentioning

confidence: 99%

Concepts of and tools for Nonlinear Time‐Series Modelling

Amendola

Francq

2009

Handbook of Computational Econometrics

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Tools and approaches are provided for nonlinear time series modelling in econometrics. A wide range of topics is covered, including probabilistic properties, statistical inference and computational methods. The focus is on the applications but the ideas of the mathematical arguments are also provided. Techniques and concepts are illustrated by various examples, Monte Carlo experiments and a real application. 1

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Baum's forward-backward algorithm revisited

Cited by 146 publications

References 4 publications

An extension of the ICA model using latent variables

An extension of the ICA model using latent variables

Estimation, Learning, and Adaptation: Systems That Improve with Use

Concepts of and tools for Nonlinear Time‐Series Modelling

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